Consider the following electrical circuit diagram in which nine identical resistors of 3 Ω each are connected as shown. If the reading of the ammeter A_1 is 1 ampere, answer the following questions : (a) What is the relationship between the readings of A_1 and A_3 ? Give reasons for your answer. (b) What is the relationship between the readings of A_2 and A_3 ? (c) Determine the reading of the voltmeter V_1. (c) Find the total resistance of the circuit.

ScienceCBSE Class 10 · Board exam 2023, set 31/2/1 · 4 marks · Case-based

CBSE Class 10 Science 2023: question 39

Set in the CBSE Class 10 board exam of 2023, paper 31/2/1, section E, question 39, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q39 · 4 marks · Case-basedCompetency-basedElectricity

Consider the following electrical circuit diagram in which nine identical resistors of 3 Ω each are connected as shown. If the reading of the ammeter A $_{1}$ is 1 ampere, answer the following questions :

(a)
What is the relationship between the readings of A $_{1}$ and A $_{3}$ ? Give reasons for your answer.
1 mark
(b)
What is the relationship between the readings of A $_{2}$ and A $_{3}$ ?
1 mark
(c)
Determine the reading of the voltmeter V $_{1}$ .
2 marks
OR
(c)
Find the total resistance of the circuit.
2 marks

Figure in the paper: A circuit with a battery at the bottom, ammeter A1 (marked +) in series on the left branch and ammeter A3 (marked +) in series on the right branch. Three parallel branches sit between: the first section has voltmeter V1 (marked +) across two 3 Ω resistors in parallel; the second section has voltmeter V2 (marked +) across three 3 Ω resistors in parallel; the third section has ammeter A2 (marked +) in a top branch in series with a 3 Ω resistor, in parallel with two more 3 Ω resistors and a third 3 Ω resistor, all between the same two junctions. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 31/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

In a series circuit, is the current the same or different at each point?

Hint 2

Identical resistors in parallel share the current equally. n equal resistors R in parallel give R/n.

Hint 3

Find each parallel group's resistance, then add the groups in series. V₁ is the main current × the first group's resistance.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(a) The readings are equal: $A_{1} = A_{3} = 1$ A. Both ammeters are in series in the main circuit, and the same current flows through every part of a series circuit.
1 mark
(b) The main current of 1 A divides equally among the four identical 3 Ω resistors in parallel. So $A_{2} = \frac{1}{4} A_{3} = 0.25$ A, i.e. $A_{2} < A_{3}$ .
1 mark
(c) For two 3 Ω resistors in parallel: $\frac{1}{R _{p}} = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ , so $R_{p} = \frac{3}{2} = 1.5 Ω$
1 mark
Using $V = I R$ : $V_{1} = 1 A \times 1.5 Ω = 1.5$ V
1 mark
(c) OR – Section 1 (two in parallel): $\frac{1}{R _{p 1}} = \frac{1}{3} + \frac{1}{3}$ , so $R_{p 1} = \frac{3}{2} Ω$ . Section 2 (three in parallel): $\frac{1}{R _{p 2}} = \frac{3}{3}$ , so $R_{p 2} = 1 Ω$
1 mark
Section 3 (four in parallel): $\frac{1}{R _{p 3}} = \frac{4}{3}$ , so $R_{p 3} = \frac{3}{4} Ω$ . The sections are in series: $R = \frac{3}{2} + 1 + \frac{3}{4} = \frac{13}{4} = 3.25 Ω$
1 mark

Answer: (a) A₁ = A₃ (series); (b) A₂ = ¼ A₃ = 0.25 A; (c) V₁ = 1.5 V; OR total resistance = 13/4 Ω = 3.25 Ω.

Where the marks are

A₁ = A₃ (½ mark), because both are in series (½ mark)
A₂ = ¼ of A₃ = 0.25 A, as current divides equally in four identical resistors (1 mark)
Parallel combination of two 3 Ω resistors = 1.5 Ω (1 mark)
V₁ = IR = 1.5 V (1 mark)
OR: R_p1 = 1.5 Ω, R_p2 = 1 Ω (1 mark); R_p3 = 0.75 Ω and total 3.25 Ω (1 mark)

Revise the chapter

Chapter: Electricity (notes, formulas, where marks are lost and every past question)
Topic: Resistors in Series and Parallel

Practise this chapterBoard-style questions from Electricity, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 31/2/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Science 2023: question 39

Hints

Step-by-step solution

Revise the chapter

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